We have constructed weakly localized massless models using chiral components of
two-dimensional conformal field theory [1]}, [2]}, [3]},
however, strict locality is disproved in some of them
and open in the others. The only known operator-algebraic technique to find local observables
is wedge-splitting [4]} (see Section ). This property is apparently difficult to hold
in massless models, especially known to be invalid in conformal case.
Actually, one encounters a similar problem in the form factor bootstrap
program to integrable models [5]}: one starts with a given S-matrix and
matrix coefficients of local operators are given as solutions of the so-called form factor equations.
One can easily observe that the convergence of these matrix coefficients is much worse
in massless case. Hence, in order to avoid such technical difficulty, one should
try to construct massive models (besides, the convergence of form factors is a
difficult problem even in massive models [6]}).
